New York Yankees' Zach Britton delivers a pitch during the eighth inning of the team's baseball game against the Kansas City Royals on Thursday, July 26, 2018, in New York.(Photo: Frank Franklin II, AP)

On Saturday, the Yankees and the lefty reliever agreed to a three-year, $39 million contract according to a person with knowledge of the negotiations.

The official deal is pending a physical.

The contract language calls for Britton to receive $13 million in each of the first three years of the deal.

Britton, 31, has the right to opt out of the deal after two years if the Yankees do not trigger the option for the 2022 season. The full, four-year pact would be worth $53 million.

With this move, the Yankees have returned another elite end-game, with Britton, Chad Green and Dellin Betances as the premier setup men to All-Star closer Aroldis Chapman.

And the Yanks might not be through adding to their bullpen, with Brooklyn-raised right-hander Adam Ottavino in their sights.

Meanwhile, the waiting game continues on Manny Machado, whose path to pinstripes remains in question.

On Friday, the Yankees officially announced a one-year deal with Troy Tulowitzki, the former five-time All-Star, with the idea that he’d open the season at shortstop – pending any further moves.

“We’re going into this with a commitment level to try Troy Tulowitzki at shortstop,’’ Yankees general manager Brian Cashman said on Friday, having been satisfied of Tulowitzki’s health.

The Yankees arranged a follow-up workout with Tulowitzki, after his original showcase for about a dozen clubs. According to Fancred.com writer and MLB Network insider Jon Heyman, Tulowitzki has received a full no-trade clause by the Yanks.

Having watched former Yankee relievers Andrew Miller (Cardinals) and David Robertson (Phillies) sign elsewhere, the Yankees were able to reunite with Britton – the winner of the 2016 Mariano Rivera “AL Reliever of the Year’’ award with Baltimore, saving 47 games and pitching to a 0.54 ERA in 69 games.

Entering his free-agent walk year in 2018, an offseason Achilles injury kept Britton sidelined until mid-June.

Just over a month later, the Yankees sent three minor league pitchers to the Orioles for Britton, who pitched to a 2.88 ERA in 25 games for the Yankees.

Combined in 2018, Britton went 2-0 with seven saves (10 chances) and a 3.10 ERA in 41 games, with 34 strikeouts in 40.2 innings.